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- W2416980462 abstract "A basic building block of many quantum algorithms is the Phase Estimation algorithm (PEA). It estimates an eigenphase $phi$ of a unitary operator $U$ using a copy of the corresponding eigenstate $|phirangle$. Suppose, in place of $|phirangle$, we have a copy of an approximate eigenstate $|psirangle$ whose overlap magnitude with $|phirangle$ is at least $sqrt{2/3}$. Then PEA fails with a constant probability. However, using multiple copies of $|psirangle$, the failure probaility can be made to decrease exponentially with the number of copies. In this paper, we show that as long as we can perform a selective inversion of $|psirangle$, a single copy is sufficient to estimate $phi$. An important application is to improve the spatial complexity of eigenpath traversal algorithm, a digital analogue of quantum adiabatic evolution, having applications ranging from quantum physics simulation to optimization. Here the goal is to travel a path of eigenstates of $n$ different unitary operators satisfying some conditions. The fastest algorithm is due to Boixo, Knill and Somma (BKS) which needs $Theta(ln n)$ copies of the eigenstate. Using our algorithm, BKS algorithm can work using just a single copy of the eigenstate." @default.
- W2416980462 created "2016-06-24" @default.
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- W2416980462 date "2012-10-17" @default.
- W2416980462 modified "2023-09-27" @default.
- W2416980462 title "Phase estimation using an approximate eigenstate" @default.
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